## A.-L. Barabási, R. Bourbonnais, M. Jensen, J. Kertesz, T. Vicsek, Y.-C. Zhang

# Multifractality of growing surfaces

#### Physical Review A 45, R6951–R6954 (1992)

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We have carried out large-scale computer stimulation of experimentally motivated (1+1)- dimensional modes of kinetic surface roughening with power-law-distributed amplitudes of uncorrelated noise. The appropriately normalized qth-order correlation function of the height differences Cq(x)=<|h(x+x')-h(x')|q> shows strong multifractal scaling behavior up to a crossover length depending on the system size, i.e. Cq(x)~xqHq, where Hq is a continuously changing nontrivial function. Beyond the crossover length conventional scaling is found.

## A.-L. Barabási, P. Szepfalusy, T. Vicsek

# Multifractal spectra of multi-affine functions

#### Physica A 178, 17–28 (1991)

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Self-affine fiunctions F(x) with multiscaling height correlations Cq(x)~XqHq are described in terrms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones. According to our calculations the f(a) type spectra are not uniquely determined by the Hq spectrum, but, depend on the particular which is made for the dependence of N on x, where N is the number of points over which the average is taken. Our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems which an underlying multiplicative process.

## A.-L. Barabási, T. Vicsek

# Multifractality of self-affine fractals

#### Physical Review A 44, 2730–2733 (1991)

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The concept of multifractality is extended to self-affine fractals in order to provide a more complete description of fractal surfaces. We show that for a class of iteratively constructed self-affine functions there exists an infinite hierarchy of exponents Hq describing the scaling of the qth order height-height correlationfunction Cq(x)~xqhq. Possible applications to random walks and turbulent flows are discussed. It is demonstratedon on the example of random walks along a chain that for stochastic lattice models leading to self-affine fractals Hq exhibits phase-transition-like behavior.

## A.-L. Barabási, L. Nitsch, I. A. Dorobantu

# On crises and supertracks: an attempt of a unified theory

#### Revue Roumanie de Physique 34, 353-357 (1989)

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An attempt is presented to study from a unified point of view crises and supertracks. The concept of n-th order crises is introduced and used to establish a general frame or describing the crises of one-dimensional maps.

## A.-L. Barabási, L. Nitsch, I.A. Dorobantu

# Supertracks and nth order windows in the chaotic regime

#### Physics Letters A 139, 53-56 (1989)

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The purpose of this paper is to generalize the concept of supertrack functions (STF), to sketch the main lines of a renormalization theory of STF and to obtain a scaling relation yielding nth order windows in the chaotic domain for the large calss of one-dimensional maps.